/* sf_erf.c -- float version of s_erf.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#include "fdlibm.h"
#include "math_config.h"

#ifdef __v810__
#define const
#endif

static const float tiny = 1e-30, half = 5.0000000000e-01, /* 0x3F000000 */
    one = 1.0000000000e+00, /* 0x3F800000 */
    two = 2.0000000000e+00, /* 0x40000000 */
    /* c = (subfloat)0.84506291151 */
    erx = 8.4506291151e-01, /* 0x3f58560b */
    /*
 * Coefficients for approximation to  erf on [0,0.84375]
 */
    efx = 1.2837916613e-01, /* 0x3e0375d4 */
    efx8 = 1.0270333290e+00, /* 0x3f8375d4 */
    pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
    pp1 = -3.2504209876e-01, /* 0xbea66beb */
    pp2 = -2.8481749818e-02, /* 0xbce9528f */
    pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
    pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
    qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
    qq2 = 6.5022252500e-02, /* 0x3d852a63 */
    qq3 = 5.0813062117e-03, /* 0x3ba68116 */
    qq4 = 1.3249473704e-04, /* 0x390aee49 */
    qq5 = -3.9602282413e-06, /* 0xb684e21a */
    /*
 * Coefficients for approximation to  erf  in [0.84375,1.25]
 */
    pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
    pa1 = 4.1485610604e-01, /* 0x3ed46805 */
    pa2 = -3.7220788002e-01, /* 0xbebe9208 */
    pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
    pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
    pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
    pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
    qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
    qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
    qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
    qa4 = 1.2617121637e-01, /* 0x3e013307 */
    qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
    qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
    /*
 * Coefficients for approximation to  erfc in [1.25,1/0.35]
 */
    ra0 = -9.8649440333e-03, /* 0xbc21a093 */
    ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
    ra2 = -1.0558626175e+01, /* 0xc128f022 */
    ra3 = -6.2375331879e+01, /* 0xc2798057 */
    ra4 = -1.6239666748e+02, /* 0xc322658c */
    ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
    ra6 = -8.1287437439e+01, /* 0xc2a2932b */
    ra7 = -9.8143291473e+00, /* 0xc11d077e */
    sa1 = 1.9651271820e+01, /* 0x419d35ce */
    sa2 = 1.3765776062e+02, /* 0x4309a863 */
    sa3 = 4.3456588745e+02, /* 0x43d9486f */
    sa4 = 6.4538726807e+02, /* 0x442158c9 */
    sa5 = 4.2900814819e+02, /* 0x43d6810b */
    sa6 = 1.0863500214e+02, /* 0x42d9451f */
    sa7 = 6.5702495575e+00, /* 0x40d23f7c */
    sa8 = -6.0424413532e-02, /* 0xbd777f97 */
    /*
 * Coefficients for approximation to  erfc in [1/.35,28]
 */
    rb0 = -9.8649431020e-03, /* 0xbc21a092 */
    rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
    rb2 = -1.7757955551e+01, /* 0xc18e104b */
    rb3 = -1.6063638306e+02, /* 0xc320a2ea */
    rb4 = -6.3756646729e+02, /* 0xc41f6441 */
    rb5 = -1.0250950928e+03, /* 0xc480230b */
    rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
    sb1 = 3.0338060379e+01, /* 0x41f2b459 */
    sb2 = 3.2579251099e+02, /* 0x43a2e571 */
    sb3 = 1.5367296143e+03, /* 0x44c01759 */
    sb4 = 3.1998581543e+03, /* 0x4547fdbb */
    sb5 = 2.5530502930e+03, /* 0x451f90ce */
    sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
    sb7 = -2.2440952301e+01; /* 0xc1b38712 */

float
erff(float x)
{
    __int32_t hx, ix, i;
    float R, S, P, Q, s, y, z, r;
    GET_FLOAT_WORD(hx, x);
    ix = hx & 0x7fffffff;
    if (!FLT_UWORD_IS_FINITE(ix)) { /* erf(nan)=nan */
        i = ((__uint32_t)hx >> 31) << 1;
        return (float)(1 - i) + one / x; /* erf(+-inf)=+-1 */
    }

    if (ix < 0x3f580000) { /* |x|<0.84375 */
        if (ix < 0x31800000) { /* |x|<2**-28 */
            if (ix < 0x04000000)
                /*avoid underflow */
                return (float)0.125 * ((float)8.0 * x + efx8 * x);
            return x + efx * x;
        }
        z = x * x;
        r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4)));
        s = one + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
        y = r / s;
        return x + x * y;
    }
    if (ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
        s = fabsf(x) - one;
        P = pa0 +
            s * (pa1 + s * (pa2 + s * (pa3 + s * (pa4 + s * (pa5 + s * pa6)))));
        Q = one +
            s * (qa1 + s * (qa2 + s * (qa3 + s * (qa4 + s * (qa5 + s * qa6)))));
        if (hx >= 0)
            return erx + P / Q;
        else
            return -erx - P / Q;
    }
    if (ix >= 0x40c00000) { /* inf>|x|>=6 */
        if (hx >= 0)
            return one - tiny;
        else
            return tiny - one;
    }
    x = fabsf(x);
    s = one / (x * x);
    if (ix < 0x4036DB6E) { /* |x| < 1/0.35 */
        R = ra0 +
            s * (ra1 +
                 s * (ra2 +
                      s * (ra3 + s * (ra4 + s * (ra5 + s * (ra6 + s * ra7))))));
        S = one +
            s * (sa1 +
                 s * (sa2 +
                      s * (sa3 +
                           s * (sa4 +
                                s * (sa5 + s * (sa6 + s * (sa7 + s * sa8)))))));
    } else { /* |x| >= 1/0.35 */
        R = rb0 +
            s * (rb1 + s * (rb2 + s * (rb3 + s * (rb4 + s * (rb5 + s * rb6)))));
        S = one +
            s * (sb1 +
                 s * (sb2 +
                      s * (sb3 + s * (sb4 + s * (sb5 + s * (sb6 + s * sb7))))));
    }
    GET_FLOAT_WORD(ix, x);
    SET_FLOAT_WORD(z, ix & 0xfffff000);
    r = expf(-z * z - (float)0.5625) * expf((z - x) * (z + x) + R / S);
    if (hx >= 0)
        return one - r / x;
    else
        return r / x - one;
}

float
erfcf(float x)
{
    __int32_t hx, ix;
    float R, S, P, Q, s, y, z, r;
    GET_FLOAT_WORD(hx, x);
    ix = hx & 0x7fffffff;
    if (!FLT_UWORD_IS_FINITE(ix)) { /* erfc(nan)=nan */
        /* erfc(+-inf)=0,2 */
        return (float)(((__uint32_t)hx >> 31) << 1) + one / x;
    }

    if (ix < 0x3f580000) { /* |x|<0.84375 */
        if (ix < 0x23800000) /* |x|<2**-56 */
            return one - x;
        z = x * x;
        r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4)));
        s = one + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
        y = r / s;
        if (hx < 0x3e800000) { /* x<1/4 */
            return one - (x + x * y);
        } else {
            r = x * y;
            r += (x - half);
            return half - r;
        }
    }
    if (ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
        s = fabsf(x) - one;
        P = pa0 +
            s * (pa1 + s * (pa2 + s * (pa3 + s * (pa4 + s * (pa5 + s * pa6)))));
        Q = one +
            s * (qa1 + s * (qa2 + s * (qa3 + s * (qa4 + s * (qa5 + s * qa6)))));
        if (hx >= 0) {
            z = one - erx;
            return z - P / Q;
        } else {
            z = erx + P / Q;
            return one + z;
        }
    }
    if (ix < 0x41e00000) { /* |x|<28 */
        x = fabsf(x);
        s = one / (x * x);
        if (ix < 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
            R = ra0 +
                s * (ra1 +
                     s * (ra2 +
                          s * (ra3 +
                               s * (ra4 + s * (ra5 + s * (ra6 + s * ra7))))));
            S = one +
                s * (sa1 +
                     s * (sa2 +
                          s * (sa3 +
                               s * (sa4 +
                                    s * (sa5 +
                                         s * (sa6 + s * (sa7 + s * sa8)))))));
        } else { /* |x| >= 1/.35 ~ 2.857143 */
            if (hx < 0 && ix >= 0x40c00000)
                return two - tiny; /* x < -6 */
            R = rb0 +
                s * (rb1 +
                     s * (rb2 + s * (rb3 + s * (rb4 + s * (rb5 + s * rb6)))));
            S = one +
                s * (sb1 +
                     s * (sb2 +
                          s * (sb3 +
                               s * (sb4 + s * (sb5 + s * (sb6 + s * sb7))))));
        }
        GET_FLOAT_WORD(ix, x);
        SET_FLOAT_WORD(z, ix & 0xfffff000);
        r = expf(-z * z - (float)0.5625) * expf((z - x) * (z + x) + R / S);
        if (hx > 0)
            return r / x;
        else
            return two - r / x;
    } else {
        if (hx > 0)
            return __math_uflowf(0);
        else
            return two - tiny;
    }
}

_MATH_ALIAS_f_f(erf)

_MATH_ALIAS_f_f(erfc)
